Playing with Wolfram-Cloud/Mathematica (Series and Sums)

In this video we use the non-intuitive and controversial Numberphile video about summing 1+2+3+... and getting -1/12 as an excuse to play with Wolfram-Alpha/Mathematica Sum and Series capabilities. We start with the sort of function that was used in the Numberphile video as a weighting function or regulator (basically a damped oscillator). The sum over the weighting functions is essentially just a geometric series -- so there is a closed form. From there we play with some derivatives and some series expansions. We do indeed see the infamous -1/12 hanging about.

[@thomasblum9803]

www1.lasalle.edu/~blum/c152wks/Numberphile.pdf